🌌 torch-relativistic

The Terrell-Penrose effect reproduced computationally: a cube appears rotated, not contracted, at relativistic speeds — validated against the analytical formula arcsin(v/c) to machine precision. Same physics as Schattschneider et al. (2025).

What this is

torch-relativistic provides differentiable PyTorch implementations of special-relativistic transformations that operate on 3D geometry, point clouds, meshes, and spacetime coordinates. Everything runs on GPU and supports autograd.

Core capabilities

• Lorentz boost — transform 4D spacetime coordinates between reference frames moving at relative velocity v (LorentzBoost)
• Terrell-Penrose distortion — compute the apparent visual distortion of objects at relativistic speeds: the rotation, not the contraction (TerrellPenroseTransform, terrell_rotation_angle)
• Relativistic aberration — how observation angles shift when the observer is in motion
• Doppler shift — frequency / colour shift for approaching and receding sources, including the transverse (time-dilation) component
• Lorentz factor (gamma), time dilation, length contraction, relativistic velocity addition — all as differentiable tensor ops
• Minkowski metric, Levi-Civita tensor, spherical harmonics — for building custom relativistic computations

Use cases

Installation

uv add torch-relativistic

Development install:

git clone https://github.com/synapticore-io/torch-relativistic.git
cd torch-relativistic
uv sync --dev

Requirements: Python ≥ 3.11, PyTorch ≥ 2.0.

Quick Start

Terrell-Penrose distortion of a 3D object

import torch, math
from torch_relativistic.utils import terrell_rotation_angle

# At what angle does a cube appear rotated at 80% light speed?
v = torch.tensor(0.8)
angle = terrell_rotation_angle(v)
print(f"Apparent rotation: {math.degrees(angle):.1f}°")  # 53.1°

# This matches the analytical formula: arcsin(v/c)
assert abs(angle.item() - math.asin(0.8)) < 1e-6

Lorentz boost on spacetime coordinates

import torch
from torch_relativistic.transforms import LorentzBoost

# 4D spacetime events: (t, x, y, z)
events = torch.randn(100, 8)  # batch of 100 events, 8-dim features

boost = LorentzBoost(feature_dim=8, time_dim=0, max_velocity=0.9)
boosted = boost(events)  # transformed to a moving reference frame

Relativistic Doppler shift

import torch
from torch_relativistic.utils import relativistic_doppler_factor, calculate_gamma

v = torch.tensor(0.5)  # 50% light speed
doppler = relativistic_doppler_factor(v)
print(f"Doppler factor (head-on): {doppler:.3f}")  # blueshift for approach

# Transverse Doppler = pure time dilation
import math
gamma = calculate_gamma(v)
doppler_transverse = relativistic_doppler_factor(v, torch.tensor(math.pi / 2))
# doppler_transverse ≈ gamma (the transverse Doppler effect)

Interactive 3D visualization

# Generate an interactive demo of the Terrell-Penrose effect
uv run python examples/terrell_penrose_demo.py
# → opens examples/terrell_penrose_demo.html in your browser

Physics reference

The Terrell-Penrose effect

In 1959, James Terrell and Roger Penrose independently showed that a rapidly moving object does not appear Lorentz-contracted to an observer — instead it appears rotated by an angle

$$\theta = \arcsin(v/c)$$

This counter-intuitive result arises because photons from the far side of the object were emitted earlier (when the object was in a different position) and arrive at the same time as photons from the near side.

After 66 years as a purely theoretical prediction, the effect was first observed in the lab in May 2025 by Schattschneider et al. at TU Wien using high-speed cameras and laser pulses — the direct inspiration for this library.

Validated against analytical formulas

The terrell_rotation_angle() function matches arcsin(v/c) to machine precision at all tested velocities (see examples/terrell_penrose_demo.py):

v/c   | arcsin (deg) | torch-relativistic | match
0.50  |      30.0000 |           30.0000  | yes
0.80  |      53.1301 |           53.1301  | yes
0.95  |      71.8051 |           71.8051  | yes

API overview

torch_relativistic.transforms

torch_relativistic.utils

Experimental: ML modules

The library also includes experimental neural network modules that apply relativistic transformations inside graph, spiking, and attention layers. These are research-stage and have not yet demonstrated empirical ML benefits on tested datasets:

• torch_relativistic.gnn — RelativisticGraphConv, MultiObserverGNN
• torch_relativistic.snn — RelativisticLIFNeuron, TerrellPenroseSNN
• torch_relativistic.attention — RelativisticSelfAttention

Contributions and benchmarks on domains with intrinsic Lorentz symmetry (particle physics, relativistic simulations) are welcome.

Development

uv sync                        # install all deps
uv run pytest tests/ -v        # run 50 tests
uv run ruff check src/ tests/  # lint
uv run black src/ tests/       # format

How to Cite

@software{bethge_torch_relativistic,
  author       = {Bethge, Björn},
  title        = {{torch-relativistic: Relativistic visual effects and
                   physics simulation toolkit for PyTorch}},
  year         = {2026},
  version      = {0.2.0},
  url          = {https://github.com/synapticore-io/torch-relativistic}
}

If your work relates to the Terrell-Penrose effect, please also cite:

@article{schattschneider2025snapshot,
  author  = {Schattschneider, Peter and others},
  title   = {A Snapshot of Relativistic Motion: Visualizing the
             Terrell-Penrose Effect},
  journal = {Communications Physics},
  year    = {2025},
  doi     = {10.1038/s42005-025-02003-6}
}

Acknowledgments

• Directly inspired by the first experimental observation of the Terrell-Penrose effect by Schattschneider et al. at TU Wien (Communications Physics, May 2025)
• Grounded in Einstein's Special Theory of Relativity
• Powered by PyTorch

License

MIT — see LICENSE.